Tell us what you are trying to do?
I want to modify the H1 title used in one of my Content Templates. I'm looking to add an additional text to it for SEO purposes and this text will appear in all the posts with that Content Template.
You want to mix the title pulled dynamically with some additional static text?
Sounds like you should use the Inline Field option to insert the dynamic title (rather than the normal dynamic sources option in sidebar), so that you can mix dynamic and static text.
You can do that with the Toolset Heading block, but it would also work with the core Heading block, plus those of many 3rd party blocks, too.
I'm not using Gutenberg to create the template. Is there an alternative way? Btw, I'm not sure if this is relevant but I'm not adding the H1 tag in the Content Template. It is getting pulled via the Theme.
That depends on your theme files, you need to locate theme file for outputting the post title, edit it, find and edit those PHP codes for post title, change it to what you want.